Is it possible to render the object 'selection outline', or mimic it in some way, for a particle system?
I agree, it's a very nice look.. It's easy to just get the wireframe of the cubes, but to capture all the edges created by intersecting faces without Freestyle is next to impossible in EEVEE or Cycles. There are some tricks you can pull with tightened-up AO, but none of them quite do it.
I think I would either shoot a pass in the Workbench renderer, say, displaying Object color of black, with Outline checked and set to white, to use as a mask in compositing later:

Or use the Header menu &gt; View &gt; Viewport Render Animation option to shoot the actual selection outline (perhaps with EEVEE,) bearing in mind you can create a custom theme under Edit &gt; Preferences &gt; Themes &gt; 3D View, and change the Object Selected color:

If you would rather just have the wireframe, just say, and I / someone else will come up with a variety of ways to do that.